The present invention relates to an incoming wave number estimation method, incoming wave number estimation device and radio device, and more particularly to an incoming wave number estimation method, incoming wave number estimation device and radio device for receiving incoming radio waves by an array antenna, where a plurality (=M) of antenna elements are linearly arrayed with a same element spacing, and estimating the number of incoming radio waves.
Recently research and development using an adaptive array antenna for mobile communication is receiving attention, and a plurality of antenna elements arranged in different spatial positions in a certain form is called an “array antenna”. Estimation of an incoming direction of a radio wave (may also be called a “signal” from the standpoint of signal processing), which enters the antenna, is a critical elemental technology of an adaptive array antenna. In an actual mobile communication system, signals transmitted from a user (mobile terminal) are often reflected by buildings, and enter a base station array antenna via a direct path and reflection paths. Therefore the issue of estimating incoming directions of multiple waves in a multi-path propagation environment is very important.
For estimating incoming directions of signals, a subspace based method is well known, which uses the orthogonality of a signal subspace and noise subspace, due to the advantages in terms of estimation accuracy and calculation volume. A typical example thereof is MUSIC (Multiple Signal Classification) (see Non-patent Document 1 listed on page 10). As a means of handling problems in estimating incoming directions of multiple waves having a complete correlation, a subspace based method with spatial smoothing, which is spatial smoothing based MUSIC, is well known (see Non-patent Document 2 and Non-patent Document 3 listed on page 10). These conventional subspace based methods require information on the number of signals that enter an array, since the signal subspace or noise subspace is acquired by the eigen value decomposition (EVD) of an array covariance matrix or the singular value decomposition (SVD) of an array data matrix. For this, estimating the number of incoming signals based on the receive data of an array is an absolute necessity of any incoming direction estimation method having high resolution, and is not limited to eigenvalue decomposition and singular value decomposition.
In the estimation of the number of incoming signals, an estimation method based on information theoretic criteria of AIC (Akaike Information Criterion) and MDL (Minimum Description Length), which uses the eigen value of an array covariance matrix obtained in eigenvalue decomposition or singular value decomposition, is well known (see Non-patent Document 4 listed on page 10). As a means of solving problems of estimating the number of multiple waves having complete correlation, an estimation method based on information theoretic criterion using spatial smoothing (SS) is also well known. Typical examples thereof are SS-AIC and SS-MDL (see Non-patent Document 2 and Non-patent Document 4).
In the case of the AIC and MDL methods, which estimate the number of uncorrelation signals, an array covariance matrix is determined based on the receive data of array antenna elements, the eigenvalue decomposition of the covariance matrix is performed, and the number of signals is estimated using the characteristic that the number of small eigen values is related to the number of signals. For the number of signals having correlation (including multiple waves having complete correlation), a uniform linear array is divided into sub-arrays to suppress the correlations among incoming signals, an averaging operation is performed on the covariance matrix of each sub-array, and the number of correlation signals is estimated using the characteristic that a number of small eigen values in the spatially averaged covariance matrix is related to the number of signals.
In order to show the shortcomings of the AIC and MDL methods, which are conventional methods for estimating the number of signals, the SS-AIC method and SS-MDL method for estimating the number of multiple waves, which are stated in Non-patent Document 2 and Non-patent Document 4, will be briefly described.
Here it is assumed that p number of multiplex wave narrowband signals [sk(n)] enter a uniform linear antenna which has M number of array elements at angle [θk]. An array receive signal of each element is given by the following Expression (1).y(n)=[y1(n), y2(n), . . . , yM(n)]T=As(n)+w(n) A=[a(θ1), a(θ2), . . . , a(θp), a(θk)=[1,ejω0τ(θk), . . . , ejω0(M−1)τ(θk)]T, s(n)=[s1(n), s2(n), . . . , sp(n)]T, w(n)=[w1(n), w2(n), . . . , wM(n)]T, ω0=2πf0, τ(θk)=(d/c)sin θk  (1)where f0, c and d are a frequency of the carrier wave, propagation velocity and array antenna element interval (half-wavelength) respectively. (•)T indicates transposition, and a(θk) and A are an array response vector and response matrix respectively. wi(n) is an average zero or power σ2 white Gaussian noise, which is independent for each element. In this case, the covariance matrix of the array is given by the following Expression (2).R=E{y(n)yH(n)}=ARsAH+σ2IM  (2)
E{•} and (•)H indicate an expected computation and complex conjugate transposition respectively, Rs=E[s(n)sH(n)] is a covariance matrix of the multiplex waves that enter, and IM is a unit matrix M×M. The correlation rik of the observed data yi(n) and yk(n) is defined as rik=E{yi(n)y*k(n)}. Here the relationship rik=r*ki is established. (•)* indicates a complex conjugate. The covariance matrix R of the array in Expression (2) can be clearly expressed as following.
                    R        =                  [                                                                      r                  11                                                                              r                  12                                                            …                                                              r                                      1                    ⁢                    M                                                                                                                        r                  21                                                                              r                  22                                                            …                                                              r                                      2                    ⁢                    M                                                                                                      …                                            …                                            …                                            …                                                                                      r                                      M                    ⁢                                                                                  ⁢                    1                                                                                                r                                      M                    ⁢                                                                                  ⁢                    2                                                                              …                                                              r                  MM                                                              ]                                    (        3        )            
In order to estimate the incoming directions {θk} of multiple waves having complete correlation, spatial smoothing MUSIC divides the entire uniform linear array into L number of overlapped sub-arrays having m (1≦m≦M) number of elements, as shown in FIG. 1. Here m and L are referred to as the “size of the sub-array” and the “number of sub-arrays”, and L=M−m+1. Based on Expression (1), the receive vector of the l-th sub-array yl(n) can be expressed by Expression (4).yl(n)=[yl(n),yl+1(n), . . . , yl+m−1(n)]T=AmDl−1s(n)+wl(n)Am=[αm(θ1), αm(θ2), . . . , αm(θp), αm(θk)=[1,ejω096 (θk), . . . , ejω0(m−1)τ(θk)]T, wl(n)=[wl(n),wl+1(n), . . . , wl−m+1(n)]T,  (4)
D is a diagonal matrix of which elements are exp(jω0τ(θ1), exp(jω0τ(θ2), . . . , exp(jω0τ(θp)), and l=1, 2, . . . L. am(θk) and Am are the response vector and response matrix of the sub-array. Therefore the covariance matrix of the l-th sub-array is given by Expression (5).Rl=E{yl(n)ylH(n)}=AmDl−1Rs(Dl−1)HAmH+σ2Im  (5)If the covariance matrix of L number of sub-arrays {Rl} is spatially averaged, the covariance matrix shown in Expression (6) is obtained.
                              R          _                =                              1            L                    ⁢                                    ∑                              l                =                1                            L                        ⁢                          R              l                                                          (        6        )            The spatially averaged eigenvalue decomposition of the covariance matrix of the above expression can be expressed as the following Expression (7).
                              R          _                =                                            ∑                              i                =                1                            m                        ⁢                                          λ                i                            ⁢                              e                i                            ⁢                              e                i                H                                              =                      E            ⁢                                                  ⁢            Λ            ⁢                                                  ⁢                          E              H                                                          (        7        )            Here ei and λi are the eigen vector and eigen value of the matrix R respectively, E is a matrix of which column is [ei], and Λ is a diagonal matrix of which elements are [λi], λ1≧λ2≧ . . . ≧λp>λp+1= . . . =λm=σ2. Hence the number of incoming signals p (=m−a) can be estimated from the number of minimum eigen values a(=m−p). Because of this, a sample covariance matrix of each sub-array is determined by the following expression using the receive vectors {y(n)}n=1N at sample time n=1, 2, . . . N. Then Expression (5), where N=∞, can be expressed as the following Expression 8.
                                          R            ^                    l                =                              1            N                    ⁢                                    ∑                              n                =                1                            N                        ⁢                                                            y                  l                                ⁡                                  (                  n                  )                                            ⁢                                                y                  l                  H                                ⁡                                  (                  n                  )                                                                                        (        8        )            The eigen value decomposition of a spatially averaged sample covariance matrix {circumflex over (R)}l can be calculated as the following Expression (9).
                                          R            _                    ^                =                                            1              L                        ⁢                                          ∑                                  l                  =                  1                                L                            ⁢                                                R                  ^                                l                                              =                                    ∑                              i                =                1                            m                        ⁢                                                            λ                  ^                                i                            ⁢                                                e                  ^                                i                            ⁢                                                e                  ^                                i                H                                                                        (        9        )            If the number of signals is estimated using an estimated value of the eigen value {{circumflex over (λ)}i}, the AIC and MDL standards are given by the following expressions.
                              A          ⁢                                          ⁢          I          ⁢                                          ⁢                      C            ⁡                          (              k              )                                      =                                            -                              N                ⁡                                  (                                      m                    -                    k                                    )                                                      ⁢            log            ⁢                          {                                                                    (                                                                  ∏                                                  i                          =                                                      k                            +                            1                                                                          m                                            ⁢                                                                        λ                          ^                                                i                                                              )                                                        1                    /                                          (                                              m                        -                        k                                            )                                                                                                            1                                          m                      -                      k                                                        ⁢                                                            ∑                                              i                        =                                                  k                          +                          1                                                                    m                                        ⁢                                                                  λ                        ^                                            i                                                                                  }                                +                      k            ⁡                          (                                                2                  ⁢                  m                                -                k                            )                                                          (                  10          ⁢          a                )                                          M          ⁢                                          ⁢          D          ⁢                                          ⁢                      L            ⁡                          (              k              )                                      =                                            -                              N                ⁡                                  (                                      m                    -                    k                                    )                                                      ⁢            log            ⁢                          {                                                                    (                                                                  ∏                                                  i                          =                                                      k                            +                            1                                                                          m                                            ⁢                                              λ                        i                                                              )                                                        1                    /                                          (                                              m                        -                        k                                            )                                                                                                            1                                          m                      -                      k                                                        ⁢                                                            ∑                                              i                        =                                                  k                          +                          1                                                                    m                                        ⁢                                                                  λ                        ^                                            i                                                                                  }                                +                      0.5            ⁢                          k              ⁡                              (                                                      2                    ⁢                    m                                    -                  k                                )                                      ⁢            log            ⁢                                                  ⁢            N                                              (                  10          ⁢          b                )            Therefore the number of signals can be determined by an integer k, which minimizes AIC (k) or MDL (k). In other words, the number of signals is k, which satisfies the following Expression (11).
                              p          ^                =                                                            arg                ⁢                                                                  ⁢                min                            ⁢                                                                    k                    ⁢          A          ⁢                                          ⁢          I          ⁢                                          ⁢                      C            ⁡                          (              k              )                                                          (                  11          ⁢          a                )                                          p          ^                =                                            arg              ⁢                                                          ⁢              min                        k                    ⁢                                          ⁢          M          ⁢                                          ⁢          D          ⁢                                          ⁢                      L            ⁡                          (              k              )                                                          (                  11          ⁢          b                )            Here k=1, 2, . . . m.
As Expression (9) shows, the AIC or the MDL method for estimating the number of incoming signals requires the eigenvalue decomposition of the spatially averaged array covariance matrix
      R    _    ^in order to obtain the eigen value {{circumflex over (λ)}i}.
With a conventional AIC or MDL method, however, eigenvalue decomposition processing and singular value decomposition processing, which are essential, become complicated, and the calculation volume becomes enormous when the number of array elements is large, or when a changing incoming direction is estimated in real-time processing, and the calculation time becomes very long. Hence the actual application of the incoming signal number estimation method, based on conventional eigenvalue decomposition, is limited by the eigenvalue decomposition which causes a burden on calculation, and the number and the incoming directions of signals that enter the array cannot be estimated at high-speed and at high accuracy.
Moreover, in the case of a conventional AIC or MDL method, a number and incoming direction of signals that enter an array cannot be estimated at high accuracy if the receive data length of an array antenna is short, or if the signal-to-noise ratio (SNR) is low.
If the incoming direction of the signal cannot be accurately estimated, the base station cannot form the receive/transmission beam accurately, and performance of the receive and transmission system of the base station deteriorates.